You are already killing the session on both ends. If you just want to kill one session variable, you should just unset that variable instead of killing the entire session. I assume that this isn’t on different domains so they will share the same session.
Well, in your situation, it’s different. It sounds like you have a regular login page for normal users and an admin login page that can be accessed by anyone, but requires an admin account. If this is so, you want to keep the session variable different from another one since you don’t want to initially log out the normal user if you happen to log off the admin account. So, the only way I can see coming out of this is manually unsetting the variable based on the page.
Say normal user logs into their account via login.php, they go to whatever URI you redirect them to. And the same user logs into their account via admin/login.php and successfully logs into that page since they are an admin. What you don’t want to do is log off on admin/logout.php and then happen to log off the main website too.
Though I recommend just integrating this into it because it would be a much more secure system if the admin gets logged off via admin/index.php, then it would also log them off on the main website too. This is to avoid any security breach so no non-admin users can go around and screwing up people’s accounts.